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URN etd-0907106-175614 Statistics This thesis had been viewed 3210 times. Download 996 times. Author Shyr Jan Author's Email Address No Public. Department Math Year 2005 Semester 2 Degree Master Type of Document Master's Thesis Language English Page Count 22 Title THE STUDY ON JOINT RELIABILITY IMPORTANCE IN SEVERAL SYSTEMS Keyword joint reliability importance joint reliability importance Abstract The joint reliability importance (JRI) is an important measurement to indicate how two components interactively affect the system reliability. The value of JRI is positive (negative) if and only if one component becomes more important (less important) when the other works. In this thesis, we study the joint reliability importance in three kinds of systems: the $k$-out-of-$n$ system, the series-parallel system, and the consecutive 2-out-of-$n$ system.
Firstly, we study the joint reliability importance in the $k$-out-of-$n$ system and investigate its properties. We compare the JRI in the $k$-out-of-$n$ system with that in the $k$-out-of-($n+1$) system. Several errors in the paper by Hong et al are corrected. In addition, we study the JRI in the $k$-out-of-$n$ system with covariance between any two fixed components.
Secondly, we study the joint reliability importance in a series-parallel system. We show that the JRI of two components is positive (negative) when they are in the same series subsystem (in different series subsystems) of the same series-parallel subsystem, and the JRI is positive when they are in different series-parallel subsystems.
Finally, we consider the joint reliability importance in the consecutive 2-out-of-$n$ system, which is not a symmetric system. Several results of the JRI in the consecutive 2-out-of-$n$ system are presented. It is surprising that the JRI of the first and the $j$th components is equal to that of the first and the $n-j+4$th components.
Advisor Committee Hsun-Wen Chang - advisor
Files Date of Defense 2006-07-31 Date of Submission 2006-09-07